2006x2005 -1
2004x2006+2005
cach lam
Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
2006 x 2005 - 1/2004 x 2006 + 2005
= 2006 x ( 2004 + 1 ) - 1/2004 x 2006 + 2005
= 2006 x 2004 + 2006 x 2005/2004 x 2006 + 2005
= 2006 x 2004 + 2005 / 2004 x 2006 + 2005
\(\frac{2003}{2004}+\frac{2004}{2005}+\frac{2005}{2003}=1-\frac{1}{2004}+1-\frac{1}{2005}+1+\frac{2}{2003}\)
\(=3+\left(\frac{1}{2003}-\frac{1}{2004}\right)+\left(\frac{1}{2003}-\frac{1}{2005}\right)\)
Do \(\frac{1}{2003}>\frac{1}{2004}>\frac{1}{2005}.\) nên \(\left(\frac{1}{2003}-\frac{1}{2004}\right)+\left(\frac{1}{2003}-\frac{1}{2005}\right)>0\)
Vì vậy \(3+\left(\frac{1}{2003}-\frac{1}{2004}\right)+\left(\frac{1}{2003}-\frac{1}{2005}\right)>3\) (đpcm)
\(A=\frac{2003}{2004}+\frac{2004}{2005}+\frac{2005}{2003}\)
\(=(1-\frac{1}{2004})+(1-\frac{1}{2005})+(1+\frac{2}{2003})\)
\(=3+(\frac{1}{2003}+\frac{1}{2003}-\frac{1}{2004}-\frac{1}{2005})\)
Do\(\frac{1}{2003}\)>\(\frac{1}{2004}\)>\(\frac{1}{2005}\)
\(\Rightarrow\frac{1}{2003}+\frac{1}{2003}+\frac{1}{2004}+\frac{1}{2005}\)>\(0\)
\(\Rightarrow3+(\frac{1}{2003}-\frac{1}{2004}+\frac{1}{2003}-\frac{1}{2005})\)>\(3\)
\(\Rightarrow A\)>\(3\)
A=\(\frac{2006x\left(2004+1\right)-1}{2006x2004+2005}=\frac{2006x2004+2006-1}{2006x2004+2005}\)
= \(\frac{2006x2004+2005}{2006x2004+2005}=1\)
\(\frac{2006\times2005-1}{2004\times2006+2005}=\frac{2006\times\left(2004+1\right)-1}{2004\times2006+2005}=\frac{2006\times2004+2006\times1-1}{2004\times2006+2005}=\frac{2006\times2004+2005}{2006\times2004+2005}=1\)
\(\frac{2006\times2005-1}{2004\times2006+2005}=\frac{2006\times\left(2004+1\right)-1}{2004\times2006+2005}=\frac{2004\times2006+2006\times1-1}{2004\times2006+2005}\)
\(=\frac{2004\times2006+2005}{2004\times2006+2005}=1\)
(2007 – 2005) + (2003 – 2001) +...+ (7 – 5) + (3 – 1)
= 2 + 2 + ... + 2 + 2
= 2.502
= 1004
Ta chỉ việc tách ra thôi VD ta thấy L
2006x2005 = 2006x2004+2006x 1
Vây ta sẽ có cách làm như sau :
\(\frac{2006\cdot2005-1}{2004\cdot2006+2005}\)
\(=\frac{2006\cdot2004+2006\cdot1-1}{2004\cdot2006+2005}\)
\(=\frac{2006\cdot2004+2006-1}{2006\cdot2004+2005}\)
\(=\frac{2006\cdot2004+2005}{2004\cdot2006+2005}=1\)
\(\frac{2006\cdot2005-1}{2004\cdot2006+2005}=\frac{2006\cdot\left(2004+1\right)}{2004\cdot2006+2005}=\frac{2006\cdot2004+2006\cdot1-1}{2004\cdot2006+2005}=\frac{2006\cdot2004+2005}{2004\cdot2006+2005}=1\)